Two bikes, different wheel diameter

[Chiomina]

I hope this is just a simple question. You have two bikes, each different wheel diameter. Will the same effort on each bike result in the one with big wheels going faster? The rest of the parameters is not important / the same. Just interested if two people riding on the bikes with two diferent wheel diameter with the same effort/force will produce the same speed and will arrive at the same time.

Thanks a lot.

 

[Quantum Defect]

I hope this is just a simple question. You have two bikes, each different wheel diameter. Will the same effort on each bike result in the one with big wheels going faster? The rest of the parameters is not important / the same. Just interested if two people riding on the bikes with two diferent wheel diameter with the same effort/force will produce the same speed and will arrive at the same time.

Thanks a lot.

I think that the differences in friction in the hubs between a big-wheel bike (slower rpm) and a small-wheel bike (faster rpm) are some of the smallest effects that a bicycle rider must overcome. The biggest in my experience has been wind resistance. Riding to the ocean in Southern California was quite a work-out, while riding back home from the ocean was much easier -- due to the steady off-shore breeze. Cyclists in road races draft behind other riders to overcome this effect.

If you have a well-maintained hub, the wheel will naturally come to rest with the valve stem at the bottom -- another indication that friction in the hub is negligible.

Bottom line, most of a cyclist's effort is going towards overcoming wind resistance.

 

[Pythagorean]

I think rolling resistance would probably be comparable to wind resistance in addition to always being there and always working against the rider. Tires are made of energy-absorbing rubber. For a fixed tread pattern, the diameter of the wheel governs how much rubber is contacting the pavement at a given moment.

 

[A.T.]

Just interested if two people riding on the bikes with two diferent wheel diameter with the same effort/force will produce the same speed and will arrive at the same time.

Changing wheel size and keeping the rest equal, is largely equivalent to switching gears and keeping wheel size equal. Why don’t you try yourself if you can achieve the same speed in different gears?

 

[Quantum Defect]

I think rolling resistance would probably be comparable to wind resistance in addition to always being there and always working against the rider. Tires are made of energy-absorbing rubber. For a fixed tread pattern, the diameter of the wheel governs how much rubber is contacting the pavement at a given moment.

I thought that the rolling resistance would be comparable for large versus small wheels. How different is the actual "foot-print" for wheels of the same width, different diameter?

 

[Pythagorean]

I thought that the rolling resistance would be comparable for large versus small wheels. How different is the actual "foot-print" for wheels of the same width, different diameter?

Compared to variability in tread pattern and material, the difference isn't that great, but I think my reasoning is wrong because it turns out the a bigger diameter actually has less rolling resistance!

https://hadland.files.wordpress.com/2013/01/lafford-chart.jpg

Anyway, wouldn't the same thought apply to wind resistance?

 

[Quantum Defect]

[snip]

Anyway, wouldn't the same thought apply to wind resistance?

If you mean wouldn't large wheeled and small wheeled bicycles have similar/comparable wind resistance for the rider (all other things being equal), then I think that they would be quite similar -- most of your effort is being expended overcoming wind resistance, and most of the wind resistance is due to the primate sitting on top.

 

[phyzguy]

I think rolling resistance would probably be comparable to wind resistance in addition to always being there and always working against the rider.

Not true unless you're going very slowly. For a typical rider, rolling resistance and wind resistance are comparable at about 9 miles/hour. As your speed increases, wind resistance increases proportional to speed^3, so it quickly becomes dominant. At 20 miles/hour, for example, wind resistance is about 4X rolling resistance. This site has a nice calculator where you can play with the various coefficients. I ride with a guy who uses a bike with small (451 mm or about 17 inch) wheels, and he doesn't appear to notice any real difference compared to standard 700mm wheels. We ride at about 18-20 miles/hour, so I wouldn't expect it to matter.

 

[Pythagorean]

I guess it depends on how you ride. I was riding mountain bikes on forest trails when I lived in Alaska so I tended to notice rolling resistance, but not wind resistance. Of course, mountain bikes have big meaty treads on them. Since I've lived in the city, and gotten a city bike, the city bike is much easier to get going because it has smaller width tires, almost zero tread. The only time I notice wind resistance is going down hill when I get up to speeds where it's relevant, but I don't ride long distances at high speeds for sport, I ride for transportation.

But then again, none of this (or wind resistance) has anything to do with OP's dependent variable (wheel diameter). And in the discussion of wheel diameter, at least rolling resistance is measurable. Not sure how much the additional cross section of a bigger diameter will affect air resistance.

 

[DaveC426913]

In my humble opinion, I think other answers bring in confounding factors that you stated you wanted to ignore. (This is not to say that all the other factors raised are not valid - they are - I just think you're looking for the basic answer.)

So, taking the question at face-value:

Will the same effort on each bike result in the one with big wheels going faster?

The short answer is no. The same effort will result in same work done (motion of vehicle), regardless of wheel size.

 

[phyzguy]

The short answer is no. The same effort will result in same work done (motion of vehicle), regardless of wheel size.

Agreed.

 

[Nuke]

Build three test bikes, one with 0.5" diameter wheels, another with 5.0" diameter wheels and the last with 50.0" wheels, same durometer. Test on 3 surfaces, say ice rink, asphalt road, beach sand. Draw curves. Compare.

 

[A.T.]

The same effort

What is "effort"?

 

[Pythagorean]

Work, but I think the output was supposed to be speed, not work.

 

[A.T.]

Work

If work must be same, and assuming we mainly do work against drag along the same distance, then drag and thus velocity must be indeed the same too. In reality of course there is an optimal gear ratio for every human, which depends on the wheel size.

 

[Nuke]

Bigger wheels roll easier, hence 29" mountain bike wheels as opposed to the old standard 24". Maybe not on a polished surface, say ice rink.

 

[Pythagorean]

If work must be same, and assuming we mainly do work against drag along the same distance, then drag and thus velocity must be indeed the same too. In reality of course there is an optimal gear ratio for every human, which depends on the wheel size.

Hrmmm. Perhaps constant work isn't always relevant. Larger wheels have more inertia and smaller rolling resistance. Maybe their advantage is that they maintain a high top speed easier, but also take more work to get to top speed, which leads to higher average (rather than instantaneous) speeds in a situation where you have stretches with no turns or traffic. It depends on the imperfection of terrain, too, for rolling resistance to be significant (holding tread/width/etc. constant).

 

[DaveC426913]

What is "effort"?

Ask the OP what his definition is. But I'm assuming it is that which could be measured in calories burned, heart-rate or breathing rate.

The OP declares he wants to keep all factors other than wheel diameter the same - including how hard the rider works (otherwise the question becomes nonsensical).

Work, but I think the output was supposed to be speed, not work.

Re-read the opening post. Both bikes will cross the finish line at the same time and they will have covered the same distance.

If work must be same, and assuming we mainly do work against drag along the same distance, then drag and thus velocity must be indeed the same too. In reality of course there is an optimal gear ratio for every human, which depends on the wheel size.

Bigger wheels roll easier, hence 29" mountain bike wheels as opposed to the old standard 24". Maybe not on a polished surface, say ice rink.

Again with the complications.

The rest of the parameters is not important / the same. Just interested if...

Sure it's a fun question to analyze, but it's not addressing the question the OP is asking.

 

[Chiomina]

In my humble opinion, I think other answers bring in confounding factors that you stated you wanted to ignore. (This is not to say that all the other factors raised are not valid - they are - I just think you're looking for the basic answer.)

So, taking the question at face-value:

The short answer is no. The same effort will result in same work done (motion of vehicle), regardless of wheel size.

Thank you! Exactly. My question is that simple. I do not care about the wind
Effort means - you have to push in the pedals with same force/effort/work. So if all the other circumstances like wind, ground, snow, rain etc. are not important and all the other parameters are the same, will these two bikes arrive at the same time with the same effort/force/work?

 

[A.T.]

I do not care about the wind

You mean there is no aerodynamic drag at all?

with the same effort/force/work?

Effort is not defined. Force and work are different things.

With no drag and same force the smaller wheels win.
With no drag and same work there is no difference.

 

[DaveC426913]

With no drag and same force the smaller wheels win.

Why?

 

[A.T.]

Why?

If the force on the pedal is the same, and only the wheel radius is reduced, what happens to the force at the tire?

 

[DaveC426913]

With no drag and same force the smaller wheels win.

If the force on the pedal is the same, and only the wheel radius is reduced, what happens to the force at the tire?

This makes no sense. By that logic, all I have to do is decrease the tire diameter to, say, 6 inches, and, with the same effort as every other rider, I will win every race in the world hands down, until someone makes a smaller tire.

 

[A.T.]

By that logic, all I have to do is decrease the tire diameter to, say, 6 inches, and, with the same effort ....

I said nothing about "effort" (whatever that is). I said "same force on the pedal".

 

[DaveC426913]

I said nothing about "effort" (whatever that is). I said "same force on the pedal".

Let's say a rider stands on one pedal, pressing down with his weight of 160 pounds.

 

[A.T.]

Let's say a rider stands on one pedal, pressing down with his weight of 160 pounds.

And?

 

[DaveC426913]

And?

The onus is on you to defend your assertion.

All I did was suggest a way to view it in simple terms. I am not sure why you're pretending to have trouble with the concept of effort. The question as-asked is talking about a rider on a bike.

The OP's question has been answered.
With only the wheel diameter being different, the same effort put in will result in the same outcome.

 

[A.T.]

The onus is on you to defend your assertion.

Defend against what? I don't see any counter argument.

With only the wheel diameter being different, the same effort put in will result in the same outcome.

And what does "effort" mean quantitatively?

 

[gennarakis]

I think you perplex things too much. I thought this is a physics forum which requires answers to have a scientific reasoning...Thanks god here, most of the classical physics problems have a uni-vocal definition!

First of all, there wouldn't be any linear speed of the bike if they were no frictions between the wheel and the surface (ex. imagine ice...you would be making pedal, the wheel would be spinning and the bike would be idle). So, I guess that, at the original question the air friction and all other frictions like the internal bicycle frictions in the gears are neglected (I make this guess because only then this question has a qualitative physical meaning without adding specific experimental values)

So the answer can be found here (http://www.real-world-physics-problems.com/bicycle-physics.html) at the equation:

F₄=F₁(R₁R₃)/(R₂R₄)

where F₄ is the force acting on the rear wheel, F₁ is the force applied to the pedal and R₄ is the rear wheel radius.

Assuming the same friction in these different wheels and the same applied force on the pedal (F₁), the smaller the wheel (R₂) the bigger the force acting on the rear wheel (F₄) so the bike would be moving faster with a smaller wheel.

I guess people can't build vehicles with very small wheels cause then the tire would be unable to hold the weight (tires have all the same pressure of air regardless of size, for the same tire material). You could use though more smaller tires to hold the weight and have a greater speed but then comes the rolling friction in the game.

I hope I covered you..

Giannis Gennarakis

 

[A.T.]

guess people can't build vehicles with very small wheels cause then the tire would be unable to hold the weight (tires have all the same pressure of air regardless of size, for the same tire material).

Try to get fast on a bike in the lowest gear, then you see the actual reason: Decreasing the wheels size would increase the pedal speed. But humans cannot apply the same force at arbitrary speeds. Not only because it requires more power, but also for physiological reasons.

 

[syhprum1]

I think you will find that wind resistance at v^2 while the power to overcome it varies as v^3